In addition to expanding and clarifying a number of sections of the first edition, it generalizes the analysis that eliminates the noncausal pre-acceleration so that it applies to removing any pre-deceleration as well. It also introduces a robust power series solution to the equation of motion that produces an extremely accurate solution to problems such as the motion of electrons in uniform magnetic fields.
Author(s): Arthur D. Yaghjian
Edition: 3
Publisher: Springer
Year: 2022
Language: English
Pages: 210
City: Cham
Foreword
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Contents
1 Introduction and Summary of Results
2 Lorentz-Abraham Force and Power Equations
2.1 Force Equation of Motion
2.2 Power Equation of Motion
3 Derivation of Force and Power Equations
3.1 General Equations of Motion from Proper-Frame Equations
4 Internal Binding Forces
4.1 Poincaré Binding Forces
4.2 Binding Forces at Arbitrary Velocity
4.2.1 Electric Polarization Producing the Binding Forces
5 Electromagnetic, Electrostatic, Bare, Measured,and Insulator Masses
5.1 Bare Mass in Terms of Electromagnetic and Electrostatic Masses
5.1.1 Extra Momentum-Energy in Newton's Second Law of Motion for Charged Particles
5.1.2 Reason for Lorentz Setting the Bare Mass Zero
6 Transformation and Redefinition of Force-Power and Momentum-Energy
6.1 Transformation of Electromagnetic, Binding, and Bare-Mass Force-Power and Momentum-Energy
6.1.1 Total Stress-Momentum-Energy Tensor for the Charged Insulator
6.2 Redefinition of Electromagnetic Momentum and Energy
7 Momentum and Energy Relations
7.1 Hyperbolic Motion
7.2 Runaway Motion
8 Solutions to the Equation of Motion
8.1 Solution to the Equation of Rectilinear Motion
8.2 Formal Solution to the General Equation of Motion
8.3 Cause and Elimination of the Pre-acceleration
8.3.1 Cause of the Pre-acceleration
8.3.2 Elimination of the Pre-acceleration
8.3.3 Determination of the Transition Force for Rectilinear Motion
8.3.4 Motion of Charge in a Uniform Electric Field for a Finite Time
8.3.5 Conservation of Momentum-Energy in the Causal Equation of Motion
8.3.6 Causal Solution to the Parallel-Plate Capacitor
8.4 Power Series Solutions to the Equation of Motion
8.4.1 Power Series Solution to Rectilinear Equation of Motion
8.4.2 Power Series and Landau-Lifshitz Solution to General Equation of Motion
8.5 Charge Moving in a Uniform Magnetic Field
8.6 Electron in a Counterpropagating Laser Beam
8.6.1 Linearly Polarized Plane Wave
Solution for γ(1+uz/c)
Solution for γux/c
Solution for the Relativistic Factor γ, the Longitudinal Velocity uz/c, and the Transverse Velocity ux/c
Determination of the Time t in Terms of ξ
Uniform Plane Wave
Sinusoidal Envelope
8.6.2 Circularly Polarized Plane Wave
Solution for γ(1+uz/c): Circular Polarization
Solution for γux/c and γuy/c: Circular Polarization
Solution for the Relativistic Factor γ, the Longitudinal Velocity uz/c, and the Transverse Velocities ux/c and uy/c: Circular Polarization
Uniform Plane Wave: Circular Polarization
Sinusoidal Envelope: Circular Polarization
8.6.3 Conditions for the Accuracy of the LL Approximate Solution to the LAD Equation of Motion
8.6.4 The Lorentz-Force Equation of Motion
8.6.5 Quantum Effects
Quantum-Vacuum Electron-Positron Pair Production
Compton Scattering
Electron Quantum Recoil from Photon Emission
8.6.6 Regions of Validity of the Different Solutions
8.6.7 Brief Summary of the LL Solution to the Electron in a Laser Beam
8.7 The Finite Difference Equation of Motion
8.8 Renormalization of the Equation of Motion
A Derivation and Transformation of Small-Velocity Force and Power
A.1 Derivation of the Small-Velocity Force and Power
A.1.1 Derivation of the Proper-Frame Force
A.1.2 Derivation of the Small-Velocity Power
A.2 Relativistic Transformation of the Small-Velocity Forceand Power
A.2.1 Relativistic Transformation of the Proper-Frame Force
A.2.2 Relativistic Transformation of the Small-Velocity Power
A.3 Noncovariance of the Power Equation
B Derivation of Force and Power at Arbitrary Velocity
B.1 The 1/a Terms of Self Electromagnetic Force and Power
B.1.1 Evaluation of 1/a Term of Self Electromagnetic Force
B.1.2 Evaluation of 1/a Term of Self Electromagnetic Power
B.2 Radiation Reaction of Self Electromagnetic Force and Power
B.2.1 Evaluation of the Radiation Reaction Force
B.2.2 Evaluation of the Radiation Reaction Power
C Electric and Magnetic Fields in a Spherical Shell of Charge
D Derivation of the Linear Terms for the Self Electromagnetic Force
References
Index
